Optimal Laplacian regularization for sparse spectral community detection

ABSTRACT Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related to alternative state-of-the-art spectral techniques for sparse graphs. Index T erms-- Regularized Laplacian, Bethe-Hessian, spectral clustering, sparse networks, community detection 1. INTRODUCTION Community detection [1] is one of the central unsupervised learning tasks on graphs. The community detection problem has vast applications in different fields of science [2] and can be seen as the simplest form of clustering, i.e. the problem of dividing objects into similarity classes.